Special Seminar - Julius Smith, Junji Kuroda, Jack Perng, and Jonathan Abel discuss their 2010 ASA presentations
2pMU5. Efficient computational modeling of piano strings for real-time synthesis using mass-spring chains, coupled finite differences, and digital waveguide sections.
Julius Smith CCRMA, Stanford Univ., Palo Alto, CA 94305, Junji Kuroda Yamaha Corp., Jack Perng, and Jonathan Abel Stanford Univ., Palo Alto, CA 94305
In previous waveguide synthesis models for piano, longitudinal waves have been neglected, although it is known that there is audible coupling from transverse to longitudinal vibration in piano strings (see, e.g., the Conklin lectures at http://www.speech.kth.se/music/5_lectures/). A general method for accurate 3-D string simulation is the mass-spring chain [Rowland and Pask, Am. J. Physics, 1999], which reduces to half-coupled wave equations at low amplitude. At yet lower amplitudes, when string slope times string curvature can be neglected, the longitudinal and transverse waves reduce to linear superposition, for which digital waveguides are most efficient for simulation [http://ccrma.stanford.edu//~jos/pasp/]. In this presentation, a hybrid piano-string model is proposed which employs a mass-spring chain at the hammer and a digital waveguide model elsewhere.
2aMU1. Modeling the piano string as a mass-spring chain.
Junji Kuroda Corporate R&D Ctr., Yamaha Corp., 203 Matsunokijima, Iwata-shi, Shizuoka-ken 438-0192, Japan, email@example.com, Julius Smith, and Jack Perng Stanford Univ., Stanford, CA 94305
The mass-spring chain allows accurate modeling of vibrating strings in all three spatial dimensions [Rowland and Pask, Am. J. Phys. 1999]. This presentation describes striking one or more adjacent masses of such a string model with a forcing function corresponding to the piano hammer [http://www.ioc.ee/stulov/PUB.htm]. An advantage of striking a mass-string model, in which each mass may move in three dimensions, is that coupling from transverse to longitudinal modes of vibration is naturally provided.
2aMU2. A stiff mass-spring-chain model for piano strings.
Junji Kuroda Corporate R&D Ctr., Yamaha Corp., 203 Matsunokijima, Iwata-shi, Shizuoka-ken 438-0192, Japan, firstname.lastname@example.org , Julius Smith, Katarina Van Heusen, and Jack Perng CCRMA, Stanford Univ., Stanford, CA 94305
The mass-spring chain allows accurate modeling of vibrating strings in all three spatial dimensions [Rowland and Pask, Am. J. Phys. 1999]. However, such a model is for non-stiff strings. A stiff mass-spring string model is proposed, consisting of three or more cross-coupled parallel mass-spring chains.
2aMU3. Sound synthesis of the harpsichord pluck using a physical plectrum-string interaction model.
Chao-Yu J. Perng Dept. of Phys., Stanford Univ., 382 Via Pueblo Mall, Stanford, CA 94305, email@example.com, Julius O. Smith, and Thomas D. Rossing Ctr. for Comput. Res. in Music and Acoust., Stanford Univ., 94305
The harpsichord, in a broad sense, refers to the family of plucked keyboard instruments. The sound of the harpsichord tone is unique and is not mistaken for other plucked string instruments, such as the guitar. The synthesis of harpsichord sound has been done previously [Valimaki et al., EURASIP J. Appl. Signal Process. 7, 934 948 2004], where excitation signals are extracted through recorded tones. In this work, we present a revision to the harpsichord plectrum model that we proposed earlier [Chao-Yu J. Perng et al., J. Acoust. Soc. Am. 127, 1733A, 2010], one which incorporates basic friction models. The harpsichord plectrum-string interaction model is used for the sound excitation, which is then implemented with a digital waveguide to produce the synthesized plucked string tone. Our harpsichord plectrum-string interaction model allows for controllability of physical parameters that allow for a range of expressiveness. The effects in which changing the physical parameters have on the synthesized pluck sound are compared and discussed.